Automatic weight painting doesn't affect mesh
Before assigning a mesh to an armature, the deforming bones have to be marked as deforming by checking deform. When creating bones, this checkbox is enabled by default, you must have unchecked it at some point.



After that, select the mesh, then &#8679; Shift RMB select the Armature and Parent them &#9096; CtrlP e.g. with Automatic Weights. Note, how vertex groups are created for the bones, which have Deform checked.



To ensure deformation, the Deform must stay checked and the Armature modifier (created by the parenting earlier) must be visible.